I - Rules
(see AOD, p. 8)
A hero that is cursed is marked with a curse token. The hero's conquest value is increased by 1 for each curse token on him. Curse tokens are generally only discarded from the hero when the hero is killed.
Example: Runewitch Astarra has 2 curse tokens on her. Her conquest value is increased from 2 to 4, so if the overlord kills her, the heroes lose 4 conquest tokens. Of course, once she is killed, all of the curse tokens on her are discarded.